Geodesic

Theory of functions and related questions of analysis

Sommaire

S.\,M.~Nikol'skij and the Soviet School of approximation theory
p. 3-12
On the works of S.\,M.~Nikol'skij in the theory of differentiable functions of several variables
p. 12-22
On extension with preservation of smoothness class and on existence of traces of functions in spaces used in particle transport theory
p. 23-24
On the approximation of the solution of integral equations in potential theory
p. 24-25
On the membership of the gradient of a~harmonic function in S.\,M.~Nikol'skij's class
p. 25-27
Approximation of functions continuous on a~half-line by Szasz--Mirak'yan operators
p. 27-28
On the approximation of functions by harmonic polynomials
p. 28-29
On a~boundary value problem of mathematical physics for a~hyperbolic system of equations
p. 29-30
The approximation of sobolev classes of functions by sums of products of functions of fewer variables
p. 30-32
A~sharp constant in the Jackson inequality in $L^2$ in the case of a~small argument of the modulus of continuity
p. 32-33
Nonsymetric approximations and inequalities for rearrangements in extremal problems of approximation theory
p. 33-35
On inequalities for polynomials with real roots
p. 35-36
Uniform asymptotic representations of orthogonal polynomials and their derivatives
p. 36-38
Application of Banach's principle to the solution of a~certain type of integral equation
p. 38-39
On inequalities for trigonometric polynomials
p. 39-41
On approximation of the classes $C(\varepsilon)$ by linear polynomial operators
p. 41-43
On constuction of approximate solutions of boundary value problems for certain classes of ordinary differential equations
p. 43-44
Linear methods for summing Fourier--Laguerre series
p. 44-46
Approximation by a~``floating'' system of exponentials on classes of periodic smooth functions
p. 46-47
On a~constructive characterization of classes of functions admitting quasiconformal extension
p. 47-49
Convexity of Banach spaces and imbedding theorems
p. 49-50
Imbeddings of an anisotropic Sobolev space for a~domain with the flexible Horn condition
p. 50-52
Convergence tests for branching continued fractions
p. 52-53
On the absolute summability of Fourier integrals by the G.\,F.~Voronoj method
p. 53-54
On absolute summability of Fourier integrals with multipliers
p. 54-55
On boundary properties of holomorphic functions
p. 56-57
A~remark on the parabolic theorem on convergence of continued fraction
p. 57-58
The conjugate Franklin system is a~basis in the space of continuous functions
p. 58-59
Extension of functions with preservation of smoothness
p. 60-61
On an estimate of approximation of continuous functions of two variables on a~finite square by certain algebraic polynomials
p. 62-63
Linear methods of summing Fourier series and fractional difference operators
p. 63-65
Multiple powers and local approximations
p. 65-67
Approximation by infinitely differentiable functions with preservation of boundary values
p. 68-70
Asymptotic estimates of the partial sums of certain Dirichlet series
p. 70-71
A~best quadrature formula with weight for a~certain class of functions
p. 71-72
Traces of functions in Sobolev spaces with metric generated by a~symmetric norm
p. 72-73
Best approximation in the mean of multiply monotone functions
p. 74-75
Investigation of questions of approximation of convex surfaces by bilinear splines
p. 75-76
On solution of weakly singular integral equations by the method of mechanical quadratures
p. 76-77
On approximation of functions of two variables by generalized polynomials
p. 77-78
On a~geometric method of reconstructing space curves arcs of geodesic circles on cylindrical surfaces
p. 79-80
Optimal reconstruction of functions of several variables
p. 80-81
Approximation in a~Banach space by a~convergent sequence of subspaces of fixed dimension
p. 81-82
A~development of the method of quadratures for the Laplace equation and conformal mappings
p. 83-85
On approximation in the mean by multidimensional positive linear operators
p. 85-86
On a~characterization of functions in the class $C_0^\psi L_\infty$
p. 86-87
On generalized Nikol'skii--Besov spaces on the sphere
p. 87-89
On degrees of smoothness, moduli of continuity and classification of continuous functions
p. 89-90
A~direct and inverse theorem on approximation by polynomials on the $m$- dimensional ball
p. 91-92
On the approximation of functions of several variables by linear means
p. 92-93
On the imbedding of a~Nikol'skij--Besov space in a~weighted Lorentz space
p. 93-95
Nonlinear capacity and extension of differentiable functions
p. 95-96
An inverse theorem on approximation of functions by operators of extension to a~canonical domain
p. 97-98
Approximation of periodic functions by linear operators
p. 98-99
Approximate solution of nonlinear integral equations with the help of local spline approximation
p. 99-100
On best approximation of functions in the spaces~$B$ and~$H$
p. 100-103
On a certain $F$-space of analytic functions
p. 103-105
Mapping sets of locally finite length by a~rational function
p. 105-107
On the choice of knots in approximation by splines in spaces with a~weight
p. 107-108
On the theory of the Cauchy problem in the complex domain
p. 108-110
Normal solvability of linear differential operators of infinite order
p. 110-112
On the application of multiplicative systems in numerical information processing
p. 112-113
Approximation of differentiable periodic functions of two variables by Fourier sums
p. 114-115
Optimal precision quadrature formulas for computing integrals of rapidly oscillating functions
p. 115-116
Approximation of certain elementary functions in the metric of~$L$
p. 117-118
On inequalities of Nikol'skij type
p. 118-119
Optimal precison approximation of functions with singular points unknow in advance
p. 120-121
Representation of functions by Bochner--Riesz spherical means in the spaces $\varphi(L)$
p. 121-122
On imbedding theorems for spaces of differentiable functions in domains
p. 122-124
On equivalent norms in weighted spaces
p. 124-125
On hypoellipticity weight for a~class of regular operators
p. 125-127
On mean convergence of Fourier--Jacobi series with quasimonotone coefficients
p. 128-129
Integral representations and estimates for generalized differences of entire functions of exponential type
p. 129-130
On trigonometric polynomials with coefficients $+1$, $-1$,~$0$
p. 131-132
A~criterion for the existence of the $p$-limit
p. 132-133
On the theory of Riesz potentials on Lorentz spaces
p. 134-135
Differential properties of an operator of best approximation of complex-valued functions
p. 135-136
Anisotropic maximal functions and potentials in weighted Lorentz spaces
p. 136-138
Superconvex functions and multiextremal problems
p. 139-140
Fourier coefficients and densities of subsets of the series of natural numbers
p. 140-141
On differentiability properties of functions in $H^p$ on the boundary of the disk of convergence
p. 141-142
On imbedding of space of Nikol'skij--Besov type for different dimensions
p. 142-143
Integrability and strong summability of multiple trigonometric series
p. 143-144
Averaging operators and partial differential equations
p. 145-146
Integral inequalities and boundary properties of monotone functions
p. 146-147
On convergence of two-dimensional continued fractions
p. 147-148
Sharp estimates of the widths of convolution classes in the space $C_{2\pi}$
p. 148-149
On estimates of strong approximation of functions by Fourier--Čebyšev sums
p. 149-151
Sharp estimates of the Lebesgue constants of partial sums of multiple Fourier series
p. 151-152
Extremal numerical integration formulas for classes of differentiable periodic functions
p. 152-154
On the approximations of Sobolev classes of functions on~$\boldsymbol R^n$
p. 154-155
On inequalities of Bernstein--Nikol'ski type
p. 155-156
A~constructive description of certain spaces
p. 156-157
On the question of improving a~theorem of Vallee--Poussin with the help of the Pontryagin maximum principle
p. 158-159
Formulas for representing the solution manifold of some systems of complex partial differential equations
p. 159-161
On formulas for the approximate computation of integrals
p. 161-163
On a~class of functions with variable smoothness
p. 163-164
On imbedding theorems for weighted classes of differentiable functions
p. 165-166
Sufficient conditions for integrability of double trigonometric cosine series
p. 166-168
The Calderon theorem for the pair of spaces $L_1+L_\infty$ and $L_1\cap L_\infty$
p. 168-169
On a way of using the theory of approximation of functions for solving integral equations of the first kind
p. 169-171
On efficent approximation of solutions of multipoint boundary value problems
p. 171-172
On strong summability of Fourier series in systems of functions of polynomial type
p. 172-174
On singular integral convolution operators of weak type
p. 174-175
Approximation numbers and the eigenvalue problem for integral operators
p. 175-176
Asymptotic formulas for the spectrum of a~class of Sturm--Liouville boundary value problems
p. 177-178
Theorems of Szasz type on absolute convergence of multiple Fourier series of functions in a~generalized Lebesgue space
p. 178-179
Absolute and strong $p$th-power summability of double fourier series by matrix methods
p. 179-180
On an iterative spline-quadrature method for solving integral equations of the second kind
p. 181-182
On the approximation of functions by algebraic polynomials
p. 182-184
Vectors of exponential type and their applications
p. 184-185
On the best mean-square approximation, by polynomials and entire functions of exponential type, to functions with a~logarithmic singular point
p. 185-186
Atomic functions and approximation theory
p. 186-187
Approximation of continuous periodic functions by linear means of their Fourier series
p. 187-188
On the imbedding of certain classes of functions on the sphere
p. 188-190
A~problem with an integral condition for an elliptic equation with strong degeneration on the whole boundary
p. 190-192
Absolute $(B,p(y)(C,1))$-summability of a~Fourier integral
p. 192-193
Direct and inverse imbedding theorems for seminormed spaces
p. 193-195
On some inequalities for functions in eighted classes and boundary value problems with degeneracy
p. 195-197
Weighted Zygmund estimates for fractional differentiation and integration, and their applications
p. 197-198
Approximation theorems for a~class of functions
p. 199-200
Theorems of Tauberian type for matrix transformations of series
p. 200-201
On a~criterion for an element of best $(\alpha,\beta)$-approximation in the space of summable functions
p. 201-202
Approximation of periodic functions by Fourier sums
p. 202-204
On the question of Pade approximation of some special functions
p. 204-205
On local approximation by Abel--Poisson sums in Hardy spaces
p. 206-207
Sharp norm estimates on some function classes
p. 207-208
The error in multidimensional piecewise polynomial approximation
p. 208-209
On uniqueness of multiple trigonometric series
p. 210-211
On an inequality for an intermediate derivative in weighted spaces
p. 211-213
On estimates of the best bilinear approximations of periodic functions and singular numbers of integral operators
p. 213-214
Uniform approximation by algebraic polynomials of functions on the sphere of an odd-dimensional space
On the distribution of the values of some sequences of algebraic polynomials
p. 216-217
Constructive characteristics of the properties of Kernels of integral operators and the behavior of their $s$-numbers
p. 217-219
On the comparison principle for Fourier expansions and existence subspaces in the integral metric
p. 219-220
On an extension theorem for spaces of functions whose partial derviatives are summable to different powers ($\Omega\in R^n$)
p. 221-222
On the approximation of functions of the Zygmund class by conjugate Cesaro sums
p. 222-224
On a~variational method in spaces with dominant mixed derivative
p. 224-225
Application of the $A$-method to the investigation of Pade approximants of elementary functions
p. 225-226
On the approximation of nonperiodic functions by algebraic polynomials in a~eighted integral metric
p. 227-228
Weighted moduli of variation and their applications
p. 228-229
Difference operators with variable step
p. 229-230
Addendum to direct approximation theorems of S.\,M.~Nikol'skij type on an interval, and inverse theorems
p. 230-232
On the transcendence and algebraic independence of the values of some classes of analytic functions
p. 232-234
Estimation of the norm of the error functional for interpolation formulas in the Sobolev space $L_2^{(m)}$
p. 234-235
On the Fourier sums in $L_p$
p. 235-236
Аппроксимационный метод для эллиптических и параболических уравнений
p. 237-238
On the approximation of even and odd bounded $2\pi$-periodic functions by trigonometric polynomials of best uniform approximation at a~given system of points
p. 238-239